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1 \chapter{Inductively Defined Sets} |
1 \chapter{Inductively Defined Sets} |
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2 \index{inductive definition|(} |
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3 \index{*inductive|(} |
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4 |
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5 This chapter is dedicated to the most important definition principle after |
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6 recursive functions and datatypes: inductively defined sets. |
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7 |
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8 We start with a simple example \ldots . A slightly more complicated example, the |
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9 reflexive transitive closure, is the subject of {\S}\ref{sec:rtc}. In particular, |
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10 some standard induction heuristics are discussed. To demonstrate the |
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11 versatility of inductive definitions, {\S}\ref{sec:CFG} presents a case study |
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12 from the realm of context-free grammars. The chapter closes with a discussion |
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13 of advanced forms of inductive definitions. |
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3 \input{Inductive/document/Star} |
15 \input{Inductive/document/Star} |
4 \input{Inductive/document/AB} |
16 \input{Inductive/document/AB} |
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17 |
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18 \index{inductive definition|)} |
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19 \index{*inductive|)} |
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20 |
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21 \section{Advanced inductive definitions} |